84.28.5 problem 16.9

Internal problem ID [22282]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 16. Initial-value problems. Supplementary problems
Problem number : 16.9
Date solved : Thursday, October 02, 2025 at 08:37:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=x \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ y^{\prime }\left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)+y(x) = x; 
ic:=[y(1) = 0, D(y)(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\sin \left (x \right ) \sin \left (1\right )-\cos \left (x \right ) \cos \left (1\right )+x \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 15

ode=D[y[x],{x,2}]+y[x]==x; 
ic={y[1]==0,Derivative[1][y][1] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x-\cos (1-x) \end{align*}

✓ Sympy. Time used: 0.043 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x - \frac {\sin {\left (1 \right )} \sin {\left (x \right )}}{\cos ^{2}{\left (1 \right )} + \sin ^{2}{\left (1 \right )}} - \frac {\cos {\left (1 \right )} \cos {\left (x \right )}}{\cos ^{2}{\left (1 \right )} + \sin ^{2}{\left (1 \right )}} \]